ISSN 0027 1349, Moscow University Physics Bulletin, 2013, Vol. 68, No. 4, pp. 279–287. © Allerton Press, Inc., 2013. Original Russian Text © B.C. Ishkhanov, A.A. Kuznetsov, 2013, published in Vestnik Moskovskogo Universiteta. Fizika, 2013, No. 4, pp. 15–22.
The Mass Distribution of 238U Photofission Fragments B. C. Ishkhanova and A. A. Kuznetsovb a Faculty of Physics, Moscow State University, Moscow, 119991 Russia b Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia e mail: [email protected] Received April 1, 2013; in final form, April 18, 2013
Abstract—The mass distribution of the 238U photofission fragments formed under γ quanta action is ana lyzed in the range of excitation energies of a fissile nucleus from 5 to 20 MeV. The influence on the ratio of asymmetrical and symmetrical photofission of the 238U structure and excitation energy of a fissile nucleus is discussed. A combined analysis and the comparison of the behavior of the asymmetrical and symmetrical modes of fission under the action of γ quanta was conducted for the first time. The results we obtained are compared with the prediction of the multi mode model of the dependence of separate fission modes on the excitation energy of a fissile nucleus.
Keywords: photofission, mass distribution of fission fragments, gamma activation analysis. DOI: 10.3103/S0027134913040073
INTRODUCTION several works. Mainly, the works on the study of photo fission mass distributions were performed on beams of Beginning from the first works on nuclei fission, the γ mass distribution was interpreted as the superposition braking quanta; hence, difficulty arises in the com parison of results obtained under the conditions of of two fission modes, viz., symmetrical and asymmet γ rical [1]. Symmetrical fission at great excitation ener various geometries and for different converters of gies is mainly explained by the liquid drop model. The quanta. In this work we studied the behavior of fission modes under the action of braking γ quanta in the concept of the peak/plateau ratio that reflects the 238 manifestation of shell effects during fission was intro range of excitation energies of the U nucleus from 5 duced in fission physics. Asymmetrical fission of to 20MeV. The main factors that determine the char actinide nuclei at low energies is explained by the acteristics of fission products are the properties of a fis shell nucleus structure when one fragment has the sile system and the excitation energy of a compound number of protons Z and neutrons N close to the nucleus. magic numbers Z = 50 and N = 82. The development of the shell model for deformed METHOD AND PROCESSING nuclei [2] and the method of calculation of shell cor OF EXPERIMENTAL RESULTS rections to the nucleus energy [3] explained the asym metry of mass distributions as passage of the nucleus The mass distributions of 238U photofission at elec during fission through a double humped barrier. The tron energies of the accelerator at 19.5, 29.1, 48.3, and calculations of the potential energy surface of a fissile 67.7 MeV were obtained in [6]. The experiment was nucleus in deformation multidimensional space dem carried out on the beam of braking γ quants of an onstrated that a nucleus on the path from the first sad RTM 70 microtron (Research Institute of Nuclear dle point to separation into two fragments can pass Physics of Moscow State University) [7]. The braking through several trajectories, i.e., potential energy spectrum of γ quanta was formed on a 2.5 mm thick minima [4, 5]. For most actinide nuclei there are three tungsten target. A target produced from a natural 235U dominating fission modes: a symmetrical superlong and 238U isotope mixture was located immediately SL mode and asymmetrical STI and STII modes. before the tungsten target. The content of 238U These asymmetrical modes are connected with neu (99.27%) in the natural isotope mixture was higher tron shells of N = 82 fragments for SNI and N = 88 for than 235U; hence, all the results related to 238U photo STII. fission. The spectrum of braking phonons was calcu Despite the considerable investigation of the lated using the GEANT4 program [8]. Spectra of photofission process, the dependence of photofission γ quanta of residual activity of irradiated uranium tar modes on the nuclear excitation energy has not been get were measured on a germanium γ spectrometer. studied. The contributions of various components of The method of the experiment was described in previ the photofission mass distribution were estimated in ous papers [6, 9]. γ Activation experiments allow one
279 280 ISHKHANOV, KUZNETSOV
3/2(+) 97 36Kr
3/2(+)169.9 ms 97 37Rb β− n
25.1% 1/2+ 426 ms n 97 38Sr β− 0.005% 0% 8 > < 20% (27/2 )IT 3523.3 142 ms β− % .7 0 (9/2)+ <667.51 1.17 s IT β− 1/2 0 3.75 s 97 39Y β− n
0.055% (3.75 s) < 0.08% (1.17 s)
1/2+ 16.91 h 97 40Zr β− IT 1/2 743.35 52.7 ms + 9/2 0 72.1 ms 97 41Nb β−
5/2+ 97 42Mo
Fig. 1. The net of decay of nuclei–isobars with mass number A = 97. to obtain the independent and accumulated yields of N λ Y = 10 1 , separate photofission products after momentary neu 1 –λ t ()1 – e 1 1 trons are emitted. Forty chains of fission of nuclei– (1) isobars in the range of mass numbers A = 80 – 160 S N = , were analyzed. The fission chain of nuclei–isobars A = 10 –λ ()t – t –λ ()t – t ()1 2 1 1 3 1 97 is shown in Fig. 1. k1 e – e
The accumulated yield is the summed number of where N10 is the number of radioactive nuclei at the definite isotope nuclei that form immediately as a moment of radiation completion, S is the area of the result of both the division and decomposition of pater photo peak in the spectrum of residual activity during nal nuclei. In the case of the formation of division measurement, t1 is the irradiation time, t2 is the time at products with mass number A = 97 (Fig. 1) one can which measurement starts, t is the time that measure determine the accumulated Y yield of zirconium iso 3 1 ment is completed, λ is the decay constant, k is a 97 1 1 tope 40Zr formation (Fig. 2) coefficient equal to the product of the detector effi
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β− − decay + fission Fission Fission
Y1 Y2
N , λ N , λ 97 − 10 1 97 − 20 2 97 40Zr(β , 16.91h) 41Nb(β , 72.1 min) 42Mo(stable)
97 97 97 Fig. 2. Formation of nuclei–isobars of 40Zr , 41Nb and 42Mo upon decay. ciency and the quantum yield of γ quanta at γ transi determine all the yields in the chain of the β– fissions tions. of isobars with the given mass number A. However, the If the yield of the parent nuclei–isobars is known, yields of separate photofission products can be esti one can determine the independent yield of the mated using the charge distribution, namely the yield daughter nucleus i.e., the number of the definite iso dependences of separate photofission products on tope nuclei that form immediately as a result of fission. mass number. The independent Y yield of 97Nb nucleus formation The charge distribution is well approximated by the 2 41 Gauss function [10]: (Fig. 2) only as the result of photofission is determined 97 () (), MY A []()2 from the accumulated yield of 40Zr formation accord IY A Z = exp – ZZ– P /C dZ, (3) ing to the formula πC λ λ – 1t1 – 2t1 where IY(A, Z) is the independent yield of a photofis λ N λ ()λ1 e ()1 e 2 20 2 – – 1 – sion product with given A and Z, MY(A) is total yield of Y2 = λ – Y1 λ , – 2t1 – 2t1 isotopes with a given mass number, Z is the most 1 – e ()λ2 – λ1 ()1 – e p probable charge in the charge distribution, and C is the S N10λ1 width of the charge distribution. N20 = λ () λ () + (2) – 2 t2 – t1 – 2 t3 – t1 λ λ k ()e – e 2 – 1 The value of most probable charge Zp for every 2 nucleus–isobar chain was calculated using the ratio λ () λ () – 1 t2 – t1 – 1 t3 – t1 [10]: N10λ2 ()e – e – λ () λ () , λ λ – 2 t2 – t1 – 2 t3 – t1 Z ==Z ± ΔZ , Z ()Z /A ()A + ν , , (4) 2 – 1 ()e – e p UCD p UCD F F LH
where ZF and AF are the charge and mass of the fissile where λ , λ are decay constants of 97Zr and 97Nb iso 1 2 40 41 system, ZUCD is the most probable charge based on the topes, Y is the accumulated yield of the 97Zr isotope assumption that the ratio of the proton number and 1 40 neutrons in light and heavy fission fragments is the 97 Δ formation; Y2 is the independent yield of 41Nb isotope same as in a fissile nucleus [11], Zp is the charge polarization calculated based on systematism [10]. formation as the result of fission, and N10 and N20 are 97 97 The + and – signs correspond to the light and heavy the quantities of Zr and Nb nuclei at the moment ν ν 40 41 fragments, respectively. L and H are the numbers of that irradiation is completed. neutrons that are emitted by light and heavy fragments The independent formation yield as the result of and estimated according to the method [12]: the photofission of separate isomeric states, such as ν ν () L = 0.531 + 0.062 AL + 143 – AF , the isomeric 97Nbmeta state, can be determined in a (5) 41 ν = 0.53ν + 0.062()A – 143 . similar manner. H H The yield of isotopes with the given mass number A It was shown in [13, 14] that in the range of excitation is the summed yield of nuclei–isobars that form as energies up to 30 MeV the width of the charge distri result of photofission. The yield of isotopes with the bution depends weakly on the excitation energy of the given mass number A can be determined as the sum of nucleus. For 238U photofission, the width parameter accumulated yields or the accumulated yield of the C ≈ 0.8 [13]. The shape of the charge distribution of long lived nuclei situated at the end of the chain of β– nuclei–isobars with mass number A = 97 of 238U fis fissions of isobars with a given mass number or as the sion is shown in Fig. 3. It is evident from the charge sum of the independent yields of the nuclei with a distribution that to determine the total yield of given mass number. The method does not allow one to nuclei–isobars with mass number A = 97 it is enough
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Yield ANALYSIS AND DISCUSSION OF RESULTS 1.0 IY The deformation of a 238U nucleus in the ground CY state is distinctly manifested by the cross section of interactions with photons. Figure 4 shows the cross 0.5 section of photon interactions with the 238U nucleus in the range of energies of giant dipole resonance (5– 19 MeV). The main decay channels of giant dipole resonance in this area are the reactions with the ejec 0 35 36 37 38 39 40 41 42 z tion one or two neutrons and nuclear fission. In the photoabsorption cross section two maxima are seen at energies of about 10 and 12.5 MeV, which correspond Fig. 3. The charge distribution of 238U photofission prod ucts with mass number A = 97. IY is the independent yield, to vibrations along the short and long axes of an ellip CY is the accumulated yield. soidal nucleus. The first maximum is manifested in the reaction cross section with the emission of one neu tron and nucleus fission and the second in the channel 97 with the emission of two neutrons and fission. to determine the accumulated yield of zirconium 40Zr isotope formation. The experimentally measured rela The mass distribution of the products of photofis tive accumulated yield of the formation of the zirco sion by braking 238U γ quanta with an upper spectral nium isotope CY()97Zr = 0.130 ± 0.004, the indepen boundary of 29.1 MeV is presented in Fig. 5. The mass 40 distribution of fission fragments gives unique informa 97 dent yield of the niobium isotope IY()41Nb =tion about the mechanism of fission of atomic nuclei. 0.00057 ± 0.00046 upon fission of 238U with an accel First, the mechanism of nuclei fission was described erator electron energy of 29.1 MeV. via the drop nucleus model [16, 17]. In the model of a liquid drop the most energetic advantageous nuclear The nuclei that form as the result of nuclear fission shape is spherical. A spherical nucleus should be are strongly overloaded with neutrons. Hence, they are mainly divided into two fragments that are equal in not stable relative to β– decay. In the case where the mass. The drop model could not explain the main excitation energy of the nucleus that forms as the con peculiarity of nuclear fission, i.e., the asymmetry of sequence of β– decay is higher than the energy of neu the mass distribution. An explanation of this phenom tron detachment, the ejection of delayed neutrons enon was proposed in the nuclear shell model. A occurs. After ejection of delayed neutron the nucleus heavy fragment has a mass that is determined by two passes into another mass chain of β– decay with A' = magic numbers: 50 for protons and 82 for neutrons. A – 1. Owing to this the measured accumulated yield V. Strutiskii introduced the method of calculation of is increased in the chain A' = A – 1 and decreased in shell correction to the drop nucleus model [3] in fis the chain with A. Hence, in this work the contributions sion physics. The concept of a double humped fission from delayed neutrons were taken into consideration barrier was raised. Again, uranium isotopes were in obtaining complete mass yields. thought to be deformed in the ground state. After the The vast majority of the experimental works on introduction of shell corrections, nuclear fission was photofission have been carried out on beams of brak thought to be penetration of a double humped poten ing γ quanta. To compare the characteristics of the fis tial barrier. In the second saddle point (potential sion products obtained in different conditions the energy maximum) mirror symmetry between the frag average excitation energy of a fissile nucleus was used. ments that form the most energetically advantageous For a braking beam the average energy of the excita form becomes the nucleus form at which two frag tion of a nucleus was calculated using the formula: ments of different masses are bound by a neck. Such an approach describes the asymmetry of the mass dis T tribution of fission fragments. ()σ, () ∫EN T E γ, F E dE The resulting mass distribution can be considered 〈〉E ()T = 0 , (6) as the consequence of two collective modes of compe exc T tition resulting in asymmetric and symmetric fragment ()σ, () separation. The table shows the ratios of the asymmet ∫NTE γ, F E dE ric and symmetric fission channels that depend on the 0 maximum energy of the braking spectrum and the where N(T, E) is the number of braking γ quanta with average energy of nucleus excitation during 238U energy E at an energy of accelerator electrons T and photofission. The corresponding results obtained in σ γ, F(E) is the cross section of photofission at the other works are also presented in the table. Figure 6 energy of γ quanta E. The cross section of photofis shows the ratio of asymmetric and symmetric fission sion was taken from estimated nuclear data [15]. for 238U photofission depending on the average excita
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Cross section, @ 400
238U (g, f) 238U (g, n) 300 235U (g, 2n) 238U (g, xn)
200
100
0 5 7 9 11 13 15 17 19 Energy of γ quanta, MeV
Fig. 4. Reaction cross section of a) photofission, b) (γ, n), c) (γ, 2n) on 238U under the action of γ quanta. d) σ(γ, xn) = σ(γ, n) + σ(γ, 2n) + σ(γ, F).
FMY, on 100 graduation marks 7
6 29.1 MeV ST1 5 ST2 SL 4 SUM
3
2
1
0 80 90 100 110 120 130 140 150 160 A
Fig. 5. The approximation of the mass distribution by five Gauss curves upon 238U photofission by braking γ quanta with a 29.1 MeV upper spectrum limit. tion energy of the nucleus. The results we obtained are The ratio of asymmetric and symmetric fission seen to correlate with the general tendency to an drops exponentially in the area of excitation energies increase in the role of the symmetric mode of nucleus from 6 to 16 MeV and thereafter this ratio is not prac fission with increasing excitation energy because at tically changed. This behavior is connected with the increasing nucleus excitation energy the role of the fact that at low energies of excitation of the nucleus shell nucleus structure should decrease. either fission or a reaction with emission of one neu
MOSCOW UNIVERSITY PHYSICS BULLETIN Vol. 68 No. 4 2013 284 ISHKHANOV, KUZNETSOV
The ratio of asymmetrical and symmetrical P/V fission peculiarities of nucleus fission are explained in the depending on the maximum energy of the braking T spec multi modal model. The multi modal fission model is trum and the average energy of excitation of the nucleus 238 based on two fundamental assumptions. In the multi Eexc upon U photofission dimensional space of deformation, the nucleus can go T, MeV E , MeV P/V Paper through several paths i.e., the minima of the potential exc energy surface on the path from the first saddle point 9 6.9 310.4 ± 85.9 [18] to separation into fragments. The separation of the 10 7.6 206.9 ± 47.7 [18] nucleus into discrete fragments occurs as the result of a random neck break. Three dominant fission modes 10 7.6 192 ± 17.5 [19] of actinide nuclei exist: the symmetrical superlong SL 12 9.7 78.0 ± 7.0 [20] mode and the asymmetrical STI and STII modes; the 15 11.9 35.0 ± 4.0 [20] asymmetrical modes are connected with the neutron 16 12.4 38 [18] fragments shells N = 82 for STI and N = 88 for STII. 19.5 11.9 ± 0.3 28.0 ± 5.7 This work The total yield of isotope with the given mass num 20 13.4 24.3 ± 2.8 [21] ber A is the sum of the symmetrical and asymmetrical fission modes. Every fission mode corresponds to pen 21 13.6 23 [18] etration through a fission barrier of a definite configu 22 13.9 20 [18] ration. For every fission mode the yield is described as 25 14.4 19 ± 2 [22] Gaussian. The total yield of fragments with a given 25 14.4 16 ± 0.5 [23] mass number is determined by the relationship:
29.1 13.7 ± 0.3 14.0 ± 2.1 This work YA()= YSL()A ++YSTI()A YSTII()A 30 14.7 13.5 ± 0.9 [20] 2 ()AA– – 30 14.7 12 [23] = K exp – SL SL 2 35 15.1 11.4 [23] 2σSL 40 15.1 10.6 [23] 2 48 16.2 11 [18] ()AA– – – D + K exp – SL STI 48.3 14.4 ± 0.3 10.4 ± 1.2 This work STI 2 2σSTI 67.7 15.6 ± 0.3 9.4 ± 1.3 This work (8) 2 70 19.9 8.2 ± 0.7 [20] ()AA– – + D + K exp – SL STI STI σ2 2 STI tron is possible. At higher energies the reaction with the emission of one neutron followed by fission – 2 ()AA– SL – DSTII becomes possible. The fission threshold with prelimi + KSTII exp – 238 2 nary emission of a neutron from the U nucleus was 2σSTII demonstrated in [24] to be 12 MeV. After neutron emission the nucleus is divided with lower excitation – 2 ()AA– SL + DST2 energy: + KSTII exp – , 2σ2 ()237 ()238 bind()238 STII Eexc' U = Eexc U – En U – Tp, (7) where the Gaussian parameters K , K , K , σ , bind SL STI STII SL where En is the energy of neutron separation from σSTI, and σSTII are the amplitudes and widths of the 238 the U nucleus and Tn is the kinetic energy of the symmetrical (SL) and asymmetrical (STI, STII) fis ejected neutron. – sion modes, ASL is the most probable mass value for Side by side with a wide maximum of the gravity – – center A ≈ 139 and A ≈ 96 in the mass distribution, nar the symmetrical fission mode, ASL – DSTI, and ASL + rower maxima are observed in the region of mass num DSTI are the most probable mass values for the light and bers A = 134 and A = 101. The structure disappears in heavy fragments of the STI asymmetrical fission the region of mass numbers A = 134 and A = 101 at modes, and A– – D , A– + D are the most increasing excitation energy. All the asymmetrical SL STII SL STII component are weakly changed with an increase in the probable mass values for the light and heavy fragments energy of excitation of the nucleus. This points to the of the STII asymmetrical fission modes. fact that it is not only the Z = 50 and N = 82 spherical Figure 5 shows the approximation of the mass dis shells that play a great role in the fission process. The tribution of 238U photofission by braking γ quants with new magic number N = 88 becomes apparent in the an upper boundary of the braking spectrum of 29.1 mass distribution in the deformed potential. These MeV by five Gauss curves. We analyzed all the litera
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P/V 1000 [18] [19] [20] This work 100 [21] [22] [23]
10
1 6 8 10 12 14 16 18 20 Excitation energy, MeV
Fig. 6. The ratio of asymmetric and symmetric fission for 238U photofission depending on the average energy of the excitation nucleus. ture data on the mass distributions of photofission rier. The coefficient of passage through the barrier pre fragments in the energy range of giant dipole reso senting in the form of an inverted parabola [26] is writ nance. The obtained characteristics of the fission ten as [27] modes are presented in Fig. 7. Joint analysis of the ∞ obtained data shows that the contribution of the mode () ⑀ρ ()⑀ that is responsible for symmetrical separation on frag TEexc = ∫d gs ments grows with the increasing excitation energy of 238 (10) the U nucleus. The contribution of the STI asym 1 metrical mode drops substantially faster than the con × , 2π{}B ()Θ()⑀ + ⑀ – E tribution of the STII mode. The contribution of the 1 + exp F exc បω ()Θ()⑀ asymmetrical STII mode connected with the deform F ing neutron shell N = 86 – 88 is almost not changed. where Eexc is the energy of nucleus excitation, The total energy that is liberated in the process of Θ ⑀ បω Θ ⑀ nuclei fission is distributed between the kinetic ener BF( ( )) and F( ( )) are height and width of the fission barrier depending on the temperature of the gies of the fission fragments and their inner excitation Θ ⑀ ρ ⑀ energy, which can be characterized by the temperature nucleus ( ), and gs( ) is the level density of the of the nucleus Θ. At the penetration of the saddle point nucleus. the deformed nucleus can be in the ground and excited The inner barrier is identical for all the fission states. Excited states above a saddle point are identi modes; hence, the contribution of each mode will fied as transition states. In excited state with energy ⑀ depend on passage through the second saddle point above the barrier the nucleus has the temperature rel [27]. The ratio of asymmetrical and symmetrical fis ative to the ground state sion will be equal to coefficient ratio of passing through the fission barrier, which explains the expo ⑀ Θ()⑀ = , (9) nential dependence of the ratio of asymmetrical and ag.s. symmetrical fission on the excitation energy of the nucleus. The obtained results support the prediction of where ag.s. is the parameter of the level density [25]. the multi modal model about changes in barrier char In the static model of nuclei fission, the contribu acteristics for fission modes at different temperatures tion of each fission mode is determined by the proba and excitation energies of a compound nucleus. bility of passage through the potential barrier [4]. The The results we obtained suggest the following fac coefficient of barrier passage will depend on the num tors that influence the mass distribution of fission frag ber of transition states and their energy above the bar ments: nucleus excitation, the shape of fission barriers
MOSCOW UNIVERSITY PHYSICS BULLETIN Vol. 68 No. 4 2013 286 ISHKHANOV, KUZNETSOV
Area, % 1000
100
10
ST1 [20] ST1 This work ST2 [20] 1 ST2 This work SL [20] SL This work
0 5 7 9 11 13 15 17 19 21 23 25 Excitation energy of the nucleus, MeV
Fig. 7. The contributions of various fission modes during 238U photofission. The sum of the contributions of all the fission modes is equal to 200%. The original mass distributions were taken from this work and [20]. and the temperature of the compound system. These REFERENCES values have an effect on both the mass distribution of 1. A. Turkevich and J. B. Niday, Phys. Rev. , 52 (1951). fission fragments and the kinetic energies of the frag 84 ments. The currently existing experimental data do 2. B. R. Mottelson and S. G. Nilsson, Phys. Rev. 99, 1615 not allow one to make a unique conclusion about the (1955). influence of each value on the mass distribution of fis 3. V. M. Strutinsky, Nucl. Phys. A. 95, 420 (1967). sion fragments. 4. U. Brosa, S. Grossmann and A. Müller, Physics Reports. 197, 167 (1990). CONCLUSIONS 5. P. Möller, A. J. Sierk, T. Ichikawa, A. Iwamoto, R. Bengtsson, H. Uhrenholt, and S. Aberg, Phys. Rev. A combined analysis and a comparison of symmet C. 79, 064304 (2009). rical and asymmetrical fission mode behavior under γ 6. B. S. Ishkhanov and A. A. Kuznetsov, Moscow Univ. quanta action was conducted for the first time. The Phys. Bull. 68 (1), 27 (2013). dependence of the contributions of various fission 7. V. I. Shvedunov, A. N. Ermakov, I. V. Gribov, E. A. Knapp, modes on the excitation energy of a fissile nucleus was G. A. Novikov, N. I. Pakhomov, I. V. Shvedunov, obtained for 238U photofission for the first time. The V. S. Skachkov, N. P. Sobenin, W. P. Trower, and analysis of the mass distribution of 238U photofission V. R. Yajlijan, Nucl. Instr. Meth. Phys. Res. A. 550 39 fragments in the area of the excitation energy of giant (2005). dipole resonance points uniquely to two modes of the 8. S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, asymmetrical distribution of fission fragments. The H. Araujo, P. Arce, M. Asai, D. Axen, S. Banerjee, distribution of the excitation energy of a fissile nucleus G. Barrand, F. Behner, L. Bellagamba, J. Boudreau, between the kinetic energy of fragments and their L. Broglia, A. Brunengo, H. Burkhardt, S. Chauvie, inner excitation energy plays a crucial role in the mass J. Chuma, R. Chytracek, and G. Cooperman, Nucl. distribution of fission fragments. Instr. Meth. Phys. Res. A 506, 250 (2003). 9. S. S. Belyshev, K. A. Stopani, and A. A. Kuznetsov, Moscow Univ. Phys. Bull. 66 (4), 363 (2011). ACKNOWLEDGMENTS 10. A. C. Wahl, Atomic Data Nucl. Data Tables. 39 (1988). The authors express gratitude to V.V. Varlamov, 11. N. Sugarman and A. Turkevich, Radiochemical Stud V.I. Svedunov, V.V. Khankin, S.S. Belyshev, K.A. Sto ies: The Fission Product. 1396 (1951). pany, and A.S. Kurilik for help in these experiments, 12. H. N. Erten and N. K. Aras, J. Inorg. Nucl. Chem. 41, useful debates, and discussion of the results. 149 (1979).
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